A rotation-angle detecting device has conventionally been employed for detecting a rotation angle of a rotator, for example, a steering wheel on an automobile that rotates beyond 360° (in a predetermined rotation range). FIGS. 9 and 10 show such a prior-art device and method of detecting rotating angle. For example, WO 96/27116 is a well-known disclosure introducing the prior-art. Firstly, the device and method of the prior-art will be described hereinafter.
FIG. 9 shows the general structure of a rotation-angle detecting device. Gear 111 is coupled with steering axle (hereinafter referred as to a rotation axle) 110 of an automobile. Two gears 112 and 113 are positioned on gear 111 so as to engage therewith. Gears 112 and 113 have permanent magnets 102 and 103, respectively. Furthermore, magnetometric sensors 104 and 105 are disposed so as to face magnets 102 and 103, respectively. Sensors 104 and 105 are arranged, together with other electric components, on circuit board 106.
FIG. 10 schematically shows the relationship between the aforementioned three gears. Rotation detecting axle 110, which rotates beyond 360°, has gear 111. Gear 111 has n teeth. On the other hand, gears 112 and 113 engaging with gear 111 have m teeth, and m+1 teeth, respectively. Sensor 104 periodically detects rotation angle ψ of gear 112. Similarly, sensor 105 detects rotation angle θ of gear 113. Although the periodicity of each sensor (represented by Ω) is usually determined 180° or 360°, it is not limited thereto.
Each sensor is connected to electronic evaluation device 116, which performs calculations required for detecting angle λ of rotation axle 110. On the precondition that each of sensors 104 and 105 is defined as “an absolute-value sensor”, the two sensors detect angle ψ of gear 112 and angle θ of gear 113, immediately after the rotation-angle detecting device is turned ON. The sensors thus outputs angles ψ and θ at a turned-on moment. Prior to the calculation of angle λ of rotation axle 110, integer number “k” is obtained from the expression below by substituting angles ψ, θ, the number of teeth of gears 112, 113, and Ω:k=((m+1)·θ−m·ψ)/Ω.
And further, with the integer number k and the number of teeth of rotation detecting axle 111, angle λ is derived from the expression below:λ=(m·ψ+(m+1)·θ−(2m+1)·k·Ω)/2n. 
The aforementioned detecting device, however, receives a signal without evaluating, even if the sensors have an abnormal output. Therefore, a perceptible error can occur in measurement. Besides, the detecting device employs an amplifying circuit to amplify a low-powered output from the sensors. If the amplifying circuit improperly amplifies the signal from the sensors, the result will be the same. Such an error in measurement has often invited a problem that the rotation of the steering wheel cannot be accurately transmitted to the vehicle control system of a car. The present invention addresses the problem above. It is therefore the object to provide a rotation-angle detecting device capable of quickly detecting abnormalities occurring in the detector for detecting a rotation angle and in the amplifying circuit for amplifying the signal from the detector.